Postgresql – Replication with Repmgr + native streaming replication

Since we're using streaming replication, writes to the master will no longer go through when the standby fails.

Not necessarily the case. This is only the case when you are setting up synchronous streaming replication. Normally the master will return immediately after it writes its own log files to disk and not wait for the slave. It is then replicated out when the slave requests.

See the synchronous_commit parameter.

I don't see why you need to futz with repmgr for this.

Can two different replication plans coexist side-by-side on the same environment?

Yes, you can create many publishers for the same articles that replicates to different subscribers.

Is it possible to setup a second replication routine for this scenario (continuous transaction replication) besides the current replication schema for the existing databases?

Yes, if you are replicating a new database or subset of data to other server, it should be fine.

You need to think about if the distributor server is same on the publisher server or you are having a different distribution server.

When distributor and publishers share the same server instance, then it is highly likely that you will hit a performance bottleneck, depending on how much data you are replicating (all data vs subset of data) and your network latency between your publisher databases and subscriber databases.

Does this create a high risk for a large existing scheduled replication job? Our DBA says that this replication scenario creates a high risk for the existing replication configuration (2x a day).

As I mentioned in above answer, it depends on how much data you are replicating and the amount of transactions happening on publisher database. Better to follow your DBA recommendations if he/she has proper stats or baseline that will show the current behavior.